The Two Cases

There are exactly two cases. There is no third.

8.1 — Case 1: No records exist

The 1:1 is unbroken. Perfect symmetry. No break, no observation, no distinction.

EH cannot be asked. There is no one and nothing to pose the question. EH is neither true nor false. The question does not arise.

This case is empirically empty: it makes no predictions, answers no questions, and is consistent with no observation, because there are no observations.

The pre-state. The empty set before the symmetry break. It is what the axioms describe the breaking of. It is not an alternative to EH. It is EH’s subject.

And you are not in this case.

You are reading. You are observing. You have already broken the symmetry.

8.2 — Case 2: At least one record exists

{S, B, R, C} are satisfied (completeness and minimality, section 4). The algebraic structure embeds into reality. EH holds.

Actualised reality. The break has happened. Records exist. The question can be asked, and the answer is yes.

8.3 — Why there is no Case 3

A hypothetical Case 3 would be: records exist, but {S, B, R, C} are not satisfied. Reality contains observations but does not satisfy the conditions for observations.

A contradiction.

If records exist, the conditions for records are met. The conditions for records are {S, B, R, C} (3.2, 4). Case 3 is logically excluded.

One might object: perhaps some other set of conditions {X, Y, Z} also permits records.

Minimality forecloses this. {S, B, R, C} are minimal: every axiom is necessary. Any set of conditions permitting records must contain {S, B, R, C} as a subset. Additional conditions may exist, but they would be redundant (completeness).

The axioms are the floor. Nothing less works.

Here is the weapon: produce conditions {X, Y, Z} that permit records without containing {S, B, R, C} as a subset. Show that observation is possible without distinction, or without persistence, or without boundedness.

The argument hands you the weapon.